An envelope tracking system generates an envelope tracking signal (ETS) that is used as a reference input for a fast switched-mode power supply (Fast SMPS). In turn, the Fast SMPS uses the envelope signal to modulate a supply of a power amplifier for an increased efficiency. At present, an ETS generated by traditional methods is not fast or accurate enough for use with the long term evolution (LTE) standard wherein an envelope modulation bandwidth can be as high as 1.5 times a modulation bandwidth. In fact, a 20 MHz LTE bandwidth requires about 30 MHz envelope bandwidth, which further requires a digital sampling clock of 52 MHz or higher.
The ETS needs to be digitally scaled by a gain value to provide an equivalent amount of gain that is present between an I/Q signal and an RF envelope driving the power amplifier. The digitally scaled ETS corresponds to the RF envelope driving the power amplifier. As a result, there is a need for digital log gain to digital linear gain multiplier that receives a log gain value, converts the log gain value into a linear gain value and multiplies a digital signal to rapidly provide an accurate gain-enhanced digital signal that is usable to generate an ETS.